Effect of transversely variable thickness of an ice plate on periodic hydroelastic waves propagating in a frozen channel

Linear hydroelastic waves propagating in a frozen channel are investigated. The channel has a rectangular cross-section, finite depth and infinite length. The liquid in the channel is an inviscid, incompressible liquid and covered with ice. The ice is modelled as a thin elastic plate of variable thickness clamped to the channel walls. The thickness is constant along the channel length and varying across it. The flow induced by ice deflections is potential. The problem reduced to a problem of wave profiles across the channel and was solved using a piecewise linear approximation of a shape of the thickness. Normal modes are calculated to ensure continuous deflections, slopes, bending stresses and shear forces in the ice plate. Two thickness distributions are studied: in Case I, the thickness is constant at a middle segment and linearly increases at edge segments over the channel’s width; in Case II, the thickness linearly decreases at the edge segments. In Case I, there is one segment with the thin part of the ice cover where, as expected, the oscillations of the ice plate will be concentrated. In Case II, there are two such areas, separated by the middle segment with the thick part of the ice cover. Dispersion relations, phase and group velocities, wave profiles and strain distributions in the ice plate are studied. Results show that the properties of periodic hydroelastic waves are significantly influenced by the ice thickness distribution across the channel.